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Paper No. 05-3

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JQ Smith and PE Anderson

Conditional Independence and Chain Event Graphs

Date: December 2004

Abstract: Graphs provide an excellent framework for interrogating a symmetric model of measurement random variables to dicover its implied conditional independence structure. However many problems are asymmetric and elicited from a description about how a process unfolds rather than through a speci.cation of relationships between measurements. All asymmetric discrete models can be represented using an event tree. Here a new mixed graphical structure called the chain event graph is introduced as a function of an event tree and a set of elicited equivalence relationships. This graph is more expressive and flexible than either the Bayesian Network, equivalent in the symmetric case, or the probability decision graph. Various separation theorems are proved that enable visual recognition of implied conditional independences in a given chain event graph from its topology. The paper also shows how this graph can be used to automatically construct random vectors whose conditional independence structure faithfully re.ects its described unfolding.